IETE Journal of Research
Vol49, Nos 2 & 3, March-June, 2003, pp 97-1 11
Complex Cell-like irection Selectivity through
Spike-Timing Dependent Plasticity
RAJESH P N RAO
Department of Computer Science and Neurobiology and Behavior Program,
University of Washington, Seattle, WA 98195-2350 USA.
email: rao@cs.washington.edu
AND
TERRENCE J SEJNOWSKI
Howard Hughes Medical Institute, The Salk Institute for Biological Studies,
10010 N. Torrey Pines Road, La Jolla, CA 92037, USA and Department of Biology,
University of California at San Diego, La Jolla, CA 92037, USA.
email: terry@salk.ed~
Complex cells i n primary visual cortex exhibit highly nonlinear receptive field properties
such as phase-invariant direction selectivity and antagonistic interactions between individually
excitatory stimuli. Traditional models assume that these properties are governed by the outputs
of antecedent simple cells, but these models are at odds with studies showing that complex cells
may receive direct inputs from the lateral geniculate nucleus (LGN) or can be driven by stimuli
that fail to activate simple cells. Using a biophysically detailed model of recurrently connected
cortical neurons, we show that complex cell-like direction selectivity may emerge without
antecedent simple cell inputs, as a consequence of spike-timing dependent synaptic plasticity
during visual development. The directionally-selective receptive fields of model neurons, as
determined by reverse correlation gnd 2-bar interaction maps, were similar to those obtained
from complex cells in awake monkey primary visual cortex. These results suggest a new
interpretation of complex cells as integral components of an adaptive cortical circuit for motion
detection and prediction.
Indexing terms: Neuroscience, Visualperception, Neural networks, Motion detection,
Prediction.
1. INTRODUCTION
and many elements of it have received experimental
support [3,4].
I
N their seminal studies of cat and monkey visual cortex,
Hubel and Wiesel classified neurons in the primary
visual cortex as simple or complex based on their receptive
field properties [l, 21. Simple cells were identified as cells
that are selective for stimulus orientation and phase, while
complex cells were identified as those that respond to an
oriented stimulus regardless of its position within the cell's
receptive field. A majority of simple and complex cells are
directionally-selective i.e. they respond best to oriented
stimuli moving in a particular direction. Most complex
cells are directionally-selective throughout their receptive
fields, suggesting that their receptive fields are made
up of directionally-selective sub-units. This led Hubel
and Wiesel to suggest their well-known hierarchical
model of visual processing in which on- and offcenter cells in the LGN converge onto simple cells in the
primary visual cortex, several of which in turn feed into a
complex cell. Hubel and Wiesel's model has remained
highly influential in guiding studies of the visual cortex
However, several lines of evidence challenge the idea
that complex cell outputs are determined solely by pooling
the outputs of simple cells. First, there exists evidence for
direct LGN input to cornpiex cells without an antecedent
simple cell stage [5-81. In addition, several anatomical
studies have suggested a lack of direct monosynaptic
connections from simple to complex cells as postulated by
the hierarchical model [9, 101 (but see also [I I]). These
anatomical results are complemented by electrophysiological studies showing that certain classes of visual
stimuli drive complex cells, but not simple cells [12-141.
Finally, many complex cells continue to exhibit responses
when simple cells are silenced via pharmacological
inactivation of corresponding input cells in the LGN.
suggesting direct inputs to complex cells from the LGN
[W.
These results suggest that there exists a class of
complex cells that receive direct LGN inputs and whose
outputs are not dependent on pooled simple cell inputs.
What then is the source of the highly non-linear receptive
Paper No 191-B; Copyright O 2003 by the IETE.
97
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98
IETE JOURNAL OF RESEARCH, Vol49, Nos 2 & 3.2003
field properties of these complex cellsa?One possibility is
that the receptive field sub-units are computed within the
dendritic tree of individual complex cells, as suggested by
Mel and colleagues for orientation- and disparity-selective
complex cells [16, 171. A similar single-neuron model for
direction selectivity is possible [18], but as shown by
Anderson et a/ [19], the biophysical properties of such a
model can only account partially for the range of direction
selective responses exhibited by cortical neurons.
Here, we pursue a second possibility, namely, that the
source of the non-linear receptive field properties of
complex cells is the pattern of excitatory and inhibitory
connectivity in recurrent cortical networks. This pattern of
connectivity may emerge as a consequence of spike-timing
dependent plasticity in cortical circuits specialized for
motion detection. Motivation for such a model comes from
two fronts: (a) studies showing a strong influence of early
visual experience on the development of direction
selectivity [20, 211, and ( 6 ) recent results suggesting an
anatomical asymmetry between excitation and inhibition in
direction-selective circuits in primary visual cortex [22].
We first show, using a detailed biophysical model of a
recurrent cortical network, that an asymmetric pattern of
intracortical connections can develop as a consequence of
temporally asymmetric spike-timing dependent plasticity.
Such a form of synaptic plasticity has been observed in
recurrent cortical synapses [23], and in the hippocampus
[24,25], the tectum [26], and in layer II/III of rat
somatosensory cortex [27]. It has been shown to be useful
for learning and predicting temporal sequences [28, 291.
We show that a network of recurrently connected complex
cells can develop non-linear directionally-selective
receptive fields as a consequence of learning to predict
moving stimuli. Space-time response plots of model
complex cells to single flashed bars were found to be
similar to those of complex cells in awake monkey Vl.
Furthermore, the types of non-linear interactions
observed in awake monkey complex cells due to pairs of
successively flashed bars were also observed in the model
and could be explained on the basis of the learned pattern
of excitatory and inhibitory cohnections. These results
suggest a new interpretation of complex cells in the visual
cortex, namely, that they are vital components of an
adaptive cortical circuit geared towards motion detection
and prediction. Preliminary reports of this study appeared
as [30] and [3 11.
1.l.Experimental Results
For our simulations, we used a two-compartment
model of a cortical neuron consisting of a dendrite and a
soma-axon compartment, as depicted in Fig l a . The
compartmental model was based on a previous study that
demonstrated the ability of such a model to reproduce a
range of cortical response properties [32]. Figure in
Time of Synaptic Input(ms)
Fig 1 Model Neocortical Neuron and Window of Synaptic
Plasticity. (a) Response of the two-compartment model
neuron to Poisson distributed excitatory and inhibitory
synaptic inputs at random locations on the dendrite. (b)
Example of a backpropagating action potential in the
dendrite of the model neuron as compared to the
corresponding action potential in the soma (enlarged from
the initial portion of the trace in (a)). (c) Window for
synaptic plasticity in the model neuron obtained by varying
the delay between presynaptic stimulation and
postsynaptic spiking (negative delays refer to cases where
presynaptic stimulation occurred before the postsynaptic
spike).
RAO & SEJNOWSKI : SPIKE
TIMING
DEPENDENT
PLASTICITY
illustrates the response of the model neuron to random
excitatory and inhibitory Poisson-distributed synaptic
inputs to the dendrite (see Methods). The presence of
voltage-activated sodium channels in the dendrite allowed
backpropagation of action potentials from the soma into the
dendrite as shown in Fig Ib. These backpropagated action
potentials allowed the calculation of synaptic modifications
as a function of local changes in membrane potential, as
discussed below.
1.2. Simulating Spike-Timing Dependent Plasticity
Synaptic currents in the model were calculated using a
kinetic model of synaptic transmission [33] with model
parameters fitted to whole-cell recorded AMPA (a-amino3-hydroxy-5- methyl-4-isoxazole proprionic acid) currents
(see Methods for more details). Other inputs representing
background activity were modeled as sub-threshold
excitatory and inhibitory Poisson processes with a mean
firing rate of 3 Hz. Synaptic plasticity was simulated by
incrementing or decrementing the value for maximal
synaptic conductance by an amount proportional to the
temporal-difference in the postsynaptic membrane
potential at time instants t -t At and t - At for presynaptic
activation at time t ; this simulates a "temporal-difference"
learning rule for prediction and yields asymmetric learning
windows similar to those observed physiologically (see
[29] for more details). Figure l c shows the temporally
asymmetric learning window observed in the model when
the delay parameter At was set to 5 ms. In this case,
potentiation was observed for EPSPs that occurred between
1 and 12 ms before the postsynaptic spike, with maximal
potentiation at 6 ms. Maximal depression was observed for
EPSPs occurring 6 ms after the peak of the postsynaptic
spike and this depression gradually decreased, approaching
zero for delays greater than 10 ms. As in rat neocortical
neurons [23], Xenopus tectal neurons [26], and cultured
hippocampal neurons [24], a narrow transition zone
(roughly 3 ms in the model) separated the potentiation and
depression windows. Note that the exact duration of the
potentiation and depression windows in the model can be
adapted to match physiological data by appropriately
choosing the temporal-difference parameter At andlor
varying the distribution of active channels in the dendrite
the synapse is located on. Alternately, following [34], one
could directly use one of the physiologically observed
learning windows. This choice yields results that are
qualitatively similar to those presented here.
2.
DEVELOPMENT OF DIRECTION SELECTIVITY
THROUGH SPIKE-TIMING DEPENDENT
PLASTICITY
To illustrate how direction selective receptive fields can
emerge as a consequenceof spike-timing dependent learning,
we first simulated a simple motion detection circuit
consisting of a single chain of nine recurrently connected
excitatory cortical neurons (Fig 2n). Each neuron in the chain
99
initially rece~vedsymmetric excitatory and Inhibitory ~nputs
of the same magnitude (maximal synaptic conductance
0.003pS) from its preceding and successor neurons (Fig 20,
"Before Learning"). Excitatory and inhibitory synaptic
currents were calculated using kinetic models of synaptic
transmission based on properties of AMPA and GABA, (yaminobutyric acid A) receptors as determined from wholecell recordings (see Methods). Neurons in the network were
exposed to 100 trials of retinotopic sensory input consisting
of moving pulses of excitation in the rightward direction (5
ms pulse of excitation at each neuron). These inputs, which
approximate the depolarization caused by nonlagged
retinotopic inputs from the LGN, were s~~fficient
to elicit a
spike from each neuron.
The effects of spike-timing dependent learning on the
excitatory and inhibitory synaptic connections in the
network are shown in Fig 26 ("After Learning"). There is a
profound asymmetry in the developed pattern of excitatory
connections from the preceding and successor neurons to
neuron 0 in Fig 20. The synaptic conductances of excitatory
connections from the left-side have been strengthened while
the ones from the right-side have been weakened. This
result can be explained as follows: due to the rightward
motion of the input stimulus, neurons on the left side fire (on
average) a few milliseconds before neuron 0 while neurons
on the right side fire (on average) a few milliseconds after
neuron 0; as a result, the synaptic strength of connections
from the left side are increased while the synaptic strength
for connections from the right side are decreased, as
prescribed by the spike-timing dependent learning window
in Fig Ic. The opposite pattern of connectivity develops for
the inhibitory connections because these were modified
according to an asymmetric anti-Hebbian learning rule that
reversed the polarity of the rule i n Fig lc. Such a rule is
consistent with spike-timing dependent anti-Hebbian
plasticity observed in some classes of inhibitory
interneurons [35]. Alternatively, one could keep the level of
inhibition constant (for example, at 0.015pS) and obtain
qualitatively similar results because a decrease in the
strength of the corresponding excitatory connections, as
shown in Fig 20, would again tilt the balance in favor of
inhibition on the right side of neuron 0.
The responses of neuron 0 to rightward and leftward
moving stimuli are shown in Fig 2 r . As expected from the
learned pattern of connections, the neuron responds
vigorously to rightward motion but not to leftward motion.
Similar responses selective for rightward motion were
exhibited by other neurons comprising the network. More
interestingly, each neuron fires a few milliseconds before
the time of arrival of the input stimulus at its soma (marked
by an asterisk) due to recurrent excitation from preceding
neurons. Such predictive neural activity is characteristic of
temporally asymmetric learning rules (see, for example,
[28; 291). In contrast, motion in the non-preferred direction
triggered recurrent inhibition and little or no response from
the model neurons.
IETE JOURNAL OF RESEARCH, Vol49, Nos 2 & 3,2003
Recurrent Synapses
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Before Learning
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After Learning
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Rightward
Motion
50 ms
Leftward
Motion
(c)
Fig2 Emergence of Direction Selectiv~tyin the Model. (a) Schematic depiction of recurrent connections to a given neuron
(labeled '0') from 4 preceding and 4 successor neurons in its chain. (6)Synaptic strength of recurrent excitatory and
inhibitory connections to neuron 0 before and after learning. Note the symmetry in connections before learning and
the asymmetry in connections after spike-timing dependent learning. Synapses were adapted during 100 trials of
exposure to rightward moving stimuli. (c) Direction selective response of neuron 0 to rightward moving stimuli after
learning. Due to recurrent excitation from preceding neurons, the neuron starts firing a few milliseconds before the
expected arrival time of its input (marked by an asterisk). The dark triangle represents the time at which the input
stimulus begins its rightward motion.
RAO & SEJNOWSKI : SPIKE
TIMING
DEPENDENT
PLASTICITY
2.1. Detecting Multiple Directions of Motion
T o investigate the question of how selectivity for
different directions of motion may emerge simultaneously,
w e simulated a network comprised of two parallel chains of
neurons (see Fig 3a), each containing 55 neurons, with
mutual inhibition (dark arrows) between corresponding
pairs of neurons along the two chains. As in the previous
simulation, a given excitatory neuron received both
excitation and inhibition from its predecessors and
successors, as shown in Fig 3b for a neuron labeled '0'.
Inhibition at a given neuron was mediated by an inhibitory
interneuron (dark circle) which
excitatory
connections from neighboring excitatory neurons (Fig 3b,
~h~ interneuron received the same input
lower
pulse of excitation as the nearest excitatory neuron.
Maximum conductances for all synapses were initialized to
small positive values (dotted lines in Fig 3c). T o break the
101
symmetry between the two chains, one may: (a) select
small randomly chosen values for the synaptic
conductances in the two chains, o r (b) provide a slight bias
in the recurrent excitatory connections, s o that neurons in
one chain may fire slightly earlier than neurons in the other
chain for a given motion direction. Both alternatives
succeed in breaking symmetry during learning. W e report
here the results for alternative (b), which is supported by
experimental evidence indicating the presence of a small
amount of initial direction selectivity in cat visual cortical
neurons before e y e opening [36].
TO evaluate the consequences of synaptic plast~cityin
the two-chain
were
alternately to leftward and rightward moving stimuli for a
total of 100 trials. The excitatory connections (labeled
'EXC' in Fig 3b) were
to the
asymmetric Hebbian learning rule in Fig l c while the
Recurrent Excitatory Connections (EXC)
-4
-3
-1
-2
1
0
2
3
4
Recurrent Ihbitory Connections (INH)
I
I
I
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Input Stimulus ( R i g h t ~ a r d ) ~
-3
-2
-1
0
1
2
3
4
(b)
(a)
Neuron N1
! i
-4
Neuron N2
Neuron N2
(Left-Selective)
Neuron N 1
Rightward
Motion
30 ms
*
-
--7 -/L-----
Lethard
Motion
---_-A_/
Synapsc Numbcr
-
SynapscNumbcr
(c)
(4
Fig,3 Detecting Multiple D~rectionsof Mot~on.(a) A model network consistmg of two c h a m of recurrently connected neurons
receiving retinotopic inputs. A glven neuron receives recu~rentcxcitation and recurrent mhib~tion(white-headed arrows) as well
as inhibition (darkheaded arrows) from ~ t counterpart
s
In the other chain. (b) Recurrent connections to a given neuron (labeled
'0') arise from 4 preceding and 4 succeeding neurons in its chain. Inhibition at a given neuron IS mediated via a GABAergic
interneuron (darkened circle). (c) Synaptic strength of recurrent excitatory (EXC) and inhibitory (INH) connections to neurons
NI and N2 before (dotted lines) and after learning (solid lines). Synapses were adapted during 100 trials of exposure to
alternating leftward and rightward moving stimuli. (d) Responses of neurons N1 and N2 to rightward and leftward moving
stimuli. After learning, neuron N1 has become selective for rightward motion (as have other neurons in the same chain) while
neuron N2 has become selective for leftward motion. In the preferred direction, each neuron starts firing several milliseconds
before the input arrives at its soma (marked by an asterisk) due to recurrent excitation from preced~ngneurons. The dark triangle
represents the start of input stimulat~onin the network.
lETE JOURNAL OF RESEARCH. Vol49, Nos 2 & 3,2003
102
excitatory connections onto the inhibitory interneuron
(labeled 'INH') were modified according to the asymmetric
anti-Hebbian learning rule, as in the previous simulation.
The synaptic conductances learned by two neurons
(marked N l and N2 in Fig 3a) located at corresponding
positions in the two chains after 100 trails of exposure to the
moving stimuli are shown in Fig 3c (solid line). The
excitatory and inhibitory connections to neuron N l exhibit
a marked asymmetry, with excitation originating from
neurons on the left and inhibition from neurons on the right.
Neuron N2 exhibits the opposite pattern of connectivity.
As expected from the learned pattern of connectivity,
neuron N 1 was found to be selective for rightward motion
while neuron N 2 was selective for leftward motion (Fig 3 4 .
Moreover, when stimulus motion is in the preferred
direction, each neuron starts firing a few milliseconds
before the time of arrival of the input stimulus at its soma
(marked by an asterisk) due to recurrent excitation from
preceding neurons. Conversely, motion in the nonpreferred direction triggers recurrent inhibition from
preceding neurons as well as inhibition from the active
neuron in the corresponding position in the other chain.
Thus, the learned pattern of connectivity allows the
direction selective neurons comprising the network to
conjointly code for and predict the moving input stimulus in
each possible direction of motion.
T o test the importance of temporal order of spikes in
learning direction selectivity, we investigated whether
classical rate-based Hebbian learning [37] could also lead
to a similar pattern of asymmetry in connections and
produce direction selectivity in our network. In rate- based
Hebbian learning, a connection between two neurons is
strengthened based o n the correlation between the firing
rates of the two neurons, irrespective of the temporal order
of input and output spikes. W e used the same network as in
the previous simulation (see Fig 3n and 3b, and Fig 4 - top
panel), with an identical initial bias in the network
connectivity as shown in Fig 3 c (dotted lines). T h e network
was exposed to 100 trials of rightward and leftward moving
stimuli as before, but a rate-based Hebbian learning rule
was used for modifying the synaptic conductances. In
particular, conductances for connections onto excitatory
(inhibitory) neurons were increased (decreased) based on
correlations between pre- and postsynaptic spikes within a
Inhibitory Interneuron
Input Stimulus (Rightward)
Excitatory Synapses After Learning
-
Inhibitory Synapses After Learning
Synapses on
Neuron 0
Synapse Number
Rightward Motion
Synapse Number
Leftward Motion
Fig 4 The Effect of Rate-Based Hebbian Learning. The same network as in Fig 3, with identical initial conditions and input stimuli, was
used to test the effects of rate-based learning. The top panel depicts the recurrent connections to a given neuron (labeled '0')in the
two-chain network. The GABAergic interneuron is represented by the darkened circle. The middle panel represents the changes
in synaptic strength as a result of rate-based Hebbian learning, which relies on correlations in pre- and postsynaptic spikes
irrespective of their temporal order. Despite an initial asymmetry in the excitatory connections (dotted lines), ratebased Hebbian
learning resulted in an approximately symmetric pattern of connections. As a result, the neurons in thk two-chain network fail to
exhibit direction selective responses (bottom panel).
RAO & SEJNOWSKI : SPIKE
TIMING
DEPENDENT
PLASTICITY
30 ms temporal window regardless of the temporal order of
the spikes. As shown in Fig 4 (middle panel), despite the
initial bias in connectivity, the network fails to develop
asymmetric connections using the purely rate-based
Hebbian learning rule. Neurons in the two chains were
found to respond similarly to both leftward and rightward
moving input stimuli, demonstrating a failure to develop
direction selectivity (Fig 4, bottom panel). These results
suggest that spike-timing dependent learning mechanisms
may play a crucial role in sculpting and maintaining
direction-selective circuits in the visual cortex.
3. THE IMPORTANCE OF RECURRENT
EXCITATORY AND INHIBITORY
CONNECTIONS
T o investigate the role of recurrent excitation in the
103
model, we gradually decreased the value of the maximum
synaptic conductance between excitatory neurons in the
trained network of Fig 3, starting from 100%of the learned
values. For a stimulus moving in the preferred direction,
decreasing the amount of recurrent excitation increased the
latency of the first spike in a model neuron and decreased
the spike count until, with less than 10% of the learned
recurrent excitation, the latency equaled the arrival time of
the input stimulus and the spike count dropped to I (Fig 5a
and 5b). These results illustrate the role of recurrent
excitation in generating predictive activity in the network
and in enhancing direction selective responses by
increasing the spike count in the preferred direction.
To evaluate the role of inhibition in maintaining
direction selectivity in the model, we quantified the degree
of direction seleetivity using the direction index: I -
% Recurrent Excitation
% Recurrent Excitation
(4
(b)
60
1
Interneurons (Control)
[7 Interneurons (Inh Block)
504030-
-
-
2010-
O
0
0.2
0.4
0.6
Direction Index
(4
0.8
1
O
-0
012
7r4
. 0:6
?8
1
Direction Index
(4
.
Fig 5 The Role of Recurrent Excitation and Inhibition in Direction Selectivity. (a) & (b) Latency of the first spike and number of spikes
elicited in an excitatory neuron in the preferred direction as a function of the strength of recurrent excitation in a model network
(100% corresponds to the learned values of recurrent 'connection strength). The network ,comprised of two chaifis, each
containing 35 excitatory neurons and 35 inhibitory interneurons (mutual inhibition between corresponding neurons in the two
chains was mediated by a separate set of inhibitory neurons that were not plastic). (c) & ( 4 Distribution of direction selectivity in
the network for excitatory and inhibitory interneurons respectively with GABAergic inhibition (Control) and without
GABAergic inhibition (Inh Block) ns measured by the direct'i'on iddex: 1 - (Non-Preferred Direction Response)/(Preferl.ed
Direction Response).
104
IETE JOURNAL OF RESEARCH, Vol49, Nos 2 & 3,2003
(Number of Spikes in Non-Preferred Direction)/(Number
of Spikes in Preferred Direction). Direction indices were
calculated for a trained network consisting of two chains of
neurons, each containing 35 excitatory and 35 inhibitory
neurons. Figures 5c and 5d show the distribution of
direction indices with and without inhibition in the
network. In the control case, most of the excitatory neurons
and inhibitory interneurons receiving recurrent excitation
are highly direction selective. Blocking inhibition
significantly reduces direction selectivity in the model
neurons but does not completely eliminate it, consistent
with some previous physiological observations [38, 391.
The source of this residual direction selectivity i n the
absence of inhibition can be traced to the asymmetric
recurrent excitatory connections in the model network
which remain unaffected by the blockage of inhibition.
3.1. Comparison to Awake Monkey Complex Cell
Responses: First-Order Analysis
Similar to complex cells in primary visual cortex,
model neurons were found to be direction selective
throughout their receptive field. This phase-invariant
direction selectivity is a consequence of the fact that at each
retinotopic location, the corresponding neuron in the chain
-receives the same pattern of asymmetric excitation and
inhibition from its neighbors as any other neuron in the
chain. Thus, for a given neuron, motion in any local region
of the chain will elicit direction selective responses due to
recurrent connections from that part of the chain. This is
consistent with previous modeling studies [40] suggesting
that recurrent connections may be responsible for the
spatial-phase invariance of complex cell responses.
good qualitative agreement between the space-time
response plot for the direction-selective complex cell and
that for the model. Both space-time plots show a
progressive shortening of response onset time and an
increase in response transiency going in the preferred
direction: in the model, this is due to recurrent excitation
from progressively closer cells on the preferred side. Firing
is reduced to below background rates 40-60 ms after
stimulus onset in the upper part of the plots: in the model,
this is due to recurrent inhibition from cells on the null side.
The response transiency and shortening of response time
course appears as a slant in the space-time maps, but unlike
space-time maps in simple cells, this slant cannot be used to
predict the neuron's velocity preference (see [I81 for more
details). However, assuming a 200 pm separation between
excitatory model neurons in each chain and utilizing known
values for the cortical magnification factor in monkey
striate cortex [41], one can estimate the preferred stimulus
velocity of model neurons to be in the range of 3.1°/s in the
fovea and 27.9"/s in the periphery (at an eccentricity of 8"),
which is within the range of monkey VI velocity
preferences (IO/sto 32%) [I 8,421.
3.2. Comparison to Awake Monkey Complex Cell
Responses: Second-Order Analysis
Complex cells are known to exhibit higher-order
interactions between two successively presented stimuli.
For example, the response to two oriented bars presented
sequentially at two different positions is generally not a
linear function of the responses to the bars presented
individually. In the case of the model network, we would
expect the asymmetry in synaptic connections to give rise
to non-linear facilitation if the two bars are flashed along
The model predicts that the neuroanatomical 'the preferred direction relative to each other and a reduction
connections for a direction selective neuron should exh~bit in response for bars flashed in the opposite direction (see
a pattern of asymmetrical excitation and inhibition similar Fig 7n).
to Fig 3c. A recent study of complex cells in awake monkey
To study such 2-bar interactions in complex cells in
V1 found excitation on the preferred side of the receptive
awake
monkey V1, single bars of optimal orientation were
field and inhibition on the null side, consistent with the
flashed
within a direction selective cell's receptive field at a
pattern of connections learned by the model [18]. In this
series
of
locations along the dimension perpendicular to
study, optimally oriented bars were flashed at random
stimulus
orientation
(these experiments were conducted in
positions in a cell's receptive field, and a reverse correlation
Margaret
Livingstone's
laboratory at Harvard Medical
map was calculated from a record of eye position, spike
A
continuous
record
was kept of eye position (at
School).
occurrence, and stimulus position. Fig 6 (top panel, left)
250
Hz),
spike
occurrence
(
I
ms
resolution), and stimulus
depicts an eye-position corrected reverse correlation map
position.
A
reverse
correlation
analysis
was performed,
for a complex cell, with time on the x-axis and stimulus
after
correcting
for
eye
position,
to
produce
two-bar
position on the y-axis: each row of the map is the postinteraction
maps
as
shown
in
Fig
70.
These
maps
show
how
stimitlus time histogram of spikes elicited for a bar tlashed
the
response
to
one
stimulus
is
intluenced
by
a
preceding
at that spatial position. The map thus depicts the firing rate
of the cell as a function of the retinal position of the stimulus, as a function of the two stimulus locations. Thus,
*foreach of the plots shown, the y-axis represents the spatial
stimulus and time after stimulus onset.
position of bar 1 while thex-axis represents the position of
For comparison with these experimental data, bar 2, which was flashed after an inter-stimulus-interval
spontaneous background activity in the model was (ISI) of 56 ms after bar I. The four plots represent the
generated by incorporating Poisson-distributed random evolution of the cell's response to the two bar sequence at
excitatory and inhibitory alpha synapses on the dendrite of delays of 25 ms, 50 ms, 75 ms, and 100 ms respectively
each model neuron. As shown in Fig 6 (top panel), there is after the onset of bar 2. The average responses for the
RAO & SEJNOWSKI : SPIKE
TIMING
DEPENDENT
PLASTICITY
5
-
-
Model Neuron Nl
Awake Monkey Complex Cell
-
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- - - 0
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,
Flashed Bar Stimulus
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..
.
_
.
Fig 6 Comparison of Monkey and Model Space-Tlme Response Plots to Single Flashed Bars. (Top, Left) Seqdence of PSTHs obtained
by flashing optimally oriented bars at 20 positions across the 5"-widereceptive field (RP)of a complex cell in klert monkey V1
(from [18]). The cell's preferred direction is from the part of the RF represented at the bottom towards the top. Flash duration = 56
ms; inter-stimulus delay 100 ms; 75 stimulus presentations. (Top, Right) PSTHs obtained' from a model neuron after
stimulating the,chain of neurons at 20 positions to the left and right side of the given neuron. The lower PSTHs represent
stimulations on the preferred side2whlieupper PSFHs represent stimulationson the nbll side. (Bottom pane1)Interpretationof the
space-time plots in the model. Bars flashed on the left (preferred) side of the recorded cell (shaded) cause progressively greater
excitation i s the sti&latioq site approaches the recorded cell's location. Bars flashed ta the right of the cell cause inhibition due
to the predomibantly inhibitory'connections that develop on the right (null) side during learning
8
can develop complex-cell-like receptive field properties as
a consequence of spike-timing dependent plasticity in
cortical circuits for motion detection. The model predicts
that some direction selective complex cells should start
Facilitation (red) can be observed above the diagonal responding a few milliseconds before the preferred
line for all four plots in Fig 7b. Locations above the stimulus arrives at the retinotopic location of the neuron in
diagonal represent cases where the two bar sequence is primary visual cortex. Such predictive neural activity has
flashed in the preferred direction of the cell (see Fig 7a).A recently been reported in ganglion cells in the rabbit and
reduction in the cell's response (blue) occurs at longer salamander retina [43]; the extent to which neural
delays, predominantly at positions below the diagonal. This responses in V1 can be characterized as being predictive
is consistent with the model predictions sketched in Fig 7a. remains an interesting open question.
A repetition of the two-bar experiment in the model yielded
interaction plots that were qualitatively similar to the
The development of complex cell receptive fields in
physiological data (Fig 7c).The main differences are in the our model is activity-dependent and is based on the
time scale and magnitude of facilitation/reduction in the assumption that these receptive fields can be modified by
responses, both of which could be fine-tuned, if necessary, visual experience, either directly via moving visual stimuli
by adjusting model parameters such as the maximal or indirectly via traveling waves in the developing retina.
allowed synaptic conductance, synaptic delays, and the Such an assumption is consistent with experimental
number of neurons used in the simulated network.
evidence indicating that visual experience during a critical
period can profoundly affect the development of direction
4. CONCLUSIONS AND FUTURE WORK
selectivity in the visual cortex. For example, direction
Our results suggest that a network of cortical neurons selectivity in kittens can be influenced by selective
individual bars were subtracted from each of the plots to
show any facilitation or reduction in responses due to
sequential interactions.
IEI'E JOURNALOF RESEARCH.Vol49, Nos 2 & 3. #m
Fig 7 Two-Bar Interactions. (a) Model predictions for sequential presentation of two optimally oriented bars. Dark arrowheads
represent inhibitory connections. Facilitation is predicted when spatial position of bar 1 is greater than that of bar 2 (relative
motion in the preferred direction); a reduction in response is expected when position of bar 2 is greater than that of bar I due to
recruitment of inhibition. (6)Sequential two-bar interaction maps for adiredion selective complex cell in awake monkey V1.The
maps show the percent difference in response after subtractingthe average responses to the individual bars from the cell's two bar
response. The four plots represent the cell's response to the two bar sequence at delays of 25 ms. SO ms. 75 ms. and 100 ms
respectively after the onset of bar 2. The inter-stimulusinterval(i.s.i.) between bar 1 and bar 2 was 56 rns. (c)Two-barinteraction
maps for the model network. Note the slightly different scale bar for model data as compared to the experimental data Both
model and experimental data show qualitatively similar sequential interactions oonsistent with the expectations in (a), namely.
facilitation (red) for spatial points above the diagonal (bar 1position >bar 2 position) and a reduction in response (blue) for points
close to and below the diagonal.
exposure to a single direction of motion [20] and even
abolished by strobe rearing [21]. Although several models
for the development of direction selectivity have been
proposed [44,45], the roles of spike timing and asymmetric
Hebbian plasticity have not been previously explored. An
intatsting question currently being investigated is whether
the explicit dependence of visual development on spike
timing in o w model can account for the fact that only low
frequcnciesof stroboscopicillumination (approximately 8-
Hz or below) cause a lossof diffction selectivity.
In a recent study [22],R d g and Kao showed, using a
combination of in vivo and in v i m techniques, that
excitatory synaptic inputs to direction selective cells in
ferret primary visual corlwr
iso-directim tuned,
ananating from local regions preferring the samed i i o n
of motion. On the otha hand, up to 40% of the inhibitmy
RAO & SEJNOWSKI : SPIKE
TIMING
DEPENDENT
PLASTICITY
connections originated in cortical regions preferring the
opposite direction of motion. Such a distribution of
synaptic inputs is consistent with the pattern of connections
predicted by our model as a consequence of spike-timing
dependent plasticity. Whether the same anatomical result
holds for macaque primary visual cortex remains an open
question.
Several other models of cortical direction selectivity
based on circuit-level interactions have previously been
proposed [45-501. Most of these have been aimed at
capturing the properties of simple cells in layer IV of
primary visual cortex in anesthetized cats. For example,
Maex and Orban [48] and Suarez et a1 [SO] present models
for direction selectivity based on the idea of spatially
asymmetric connectivity and intracortical amplification.
Both of these are intended to be models of simple cell
direction selectivity. The model analyzed by Mineiro and
Zipser [49] is similar to our model, although at a more
abstract level. None of the above models addresses the
issue of how network connectivity may develop naturally
as a consequence of synaptic plasticity. Wimbauer et a1
present a model for the development of direction selectivity
in simple cells in cat striate cortex based on rate-based
Hebbian learning and laggedlnon-lagged inputs from the
LGN [45]; however, the applicability of this model to
monkey visual cortex is unclear given that there is
inconclusive evidence for laggedlnonlagged cells in
monkey LGN. A popular class of models that captures
some important properties of complex cells is the class of
spatiotemporal energy models [51,52]; these typically
utilize the squared outputs of a pair of quadrature filters that
model simple cell receptive fields. Although extremely
useful as phenomenological models, such models would
not be applicable to cases where a given complex cell
receives direct non-oriented LGN inputs.
Temporally asymmetric Hebbian learning has
previously been suggested as a possible mechanism for
sequence learning in the hippocampus [28,25] and as an
explanation for the asymmetric expansion of hippocampal
place fields during route learning [53,54]. Some of these
theories require relatively long temporal windows of
synaptic plasticity (on the order of several hundreds of
milliseconds) [28] while others have utilized temporal
windows in the sub-millisecond range for coincidence
detection [%I. Prediction and sequence learning in our
model is based on a window of plasticity in the tens of
milliseconds range which is roughly consistent with recent
physiological observations [23,24,26,27]. Although a
fixed learning window (roughly 15 ms of potentiation1
depression) was used in the simulations, the temporal
extent of this window can be modified by changing the
parameter At. The model predicts that the shape and width
of the asymmetric learning window should be a function of
the backpropagating action potentials in the dendrite that
the synapse is located on (see [29] for more details). In the
case of hippocampal neurons and cortical neurons, the
107
width of backpropagating action potentials in apical
dendrites has been reported to be in the range of 10-25
milliseconds, which is comparable to the size of
potentiationldepression windows for synapses located on
these dendrites [24,56].
In vitro experiments involving cortical and
hippocampal slices suggest the possibility of short-term
plasticity in synaptic connections onto pyramidal neurons
[57-591.The kinetic model of synaptic transmission used in
the present study can be extended to include short-term
plasticity with the addition of a parameter governing the
level of depression caused by each presynaptic action
potential [40,57,59]. The adaptation of this parameter may
allow finer control of postsynaptic firing in the model in
addition to the coarse-grained control offered by
modifications of maximal synaptic conductance. As
suggested by previous studies [40,57], we expect the
addition of synaptic depression in our model to enhance the
transient response of model neurons to stimuli such as
flashed bars (see Fig 6) and to broaden the response to
drifting stimuli, due to the reduced sensitivity of
postsynaptic neurons to mean presynaptic firing rates.
In summary, our results suggest the new hypothesis that
complex cells may play a crucial rdie in predicting and
tracking moving stimuli as part of an adaptive cortical
network for motion detection. Prediction and sequence
learning have both been previously suggested as important
goals of cortical information processing [28,60-671. Our
biophysical simulations suggest a specific mechanism for
achieving these goals in the context of visual information
processing. Given the discovery of spike-timing dependent
learning mechanisms in several different cortical areas [23,
25,271, the biophysical mechanisms investigated herein
may prove useful in studying information processing in
other cortical areas as well.
5. METHODS
5.1. Neocortical Neuron Model
Two-compartment model neocortical neurons
consisting of a dendritic compartment and a soma-axon
compartment [32] were implemented using the simulation
software Neuron (M Hines, in Neural Systems: Analysis
and Modeling, F H Eeckman, editor (Kluwer, Boston, MA,
1993), pp 127-136). Four voltage-dependent currents and
one calcium-dependent current were 'simulated: fast Na+,
I,; fast K+, IKv; slow non-inactivating K+, IK,,, ; high
voltage-activated Ca2+, Icn and calcium-dependent Kt
current, IKcn (see [32] for references). Conventional
Hodgkin-Huxley-type kinetics were used for all currents
(integration time step = 25 ~ stemperature
,
= 37" celsius).
Ionic currents I were calculated using the ohmic equation:
I = gAXB(V- E) where g is the maximal ionic conductance
density, A and B are activation and inactivation variables
respectively (x denotes the order of kinetics - see [32] for
108
IETE JOURNAL OF RESEARCH, Vol49, Nos 2 & 3,2003
further details), and E is the reversal potential for the given
ion species (EK= -90 mV, EN, = GOmV, Ec, = 140 mV,
ElCOk= -70 mV). The following active conductance
densities were used in the dendritic compartment (in pS/
pm2): gNn= 20, gcfl= 0.2, gKt,,=0.1, and gKcO
= 3, with
leak conductance 33.3 pS/cm2 and specific membrane
resistance 30 kQ-cm2. The soma-axon compartment
contained YN, = 40,000 and g, = 1400. For all compartments, the specific membrane capacitance was 0.75 pF/
cm2. Two key parameters governing the response
properties of the model neuron are [32]: the ratio of axosomatic area to dendritic membrane area (p) and the
coupling resistance between the two compartments ( K ) .
For the present simulations, we used the values p = 150
(with an area of 100 pm"or the soma-axon compartment)
and a coupling resistance of K = 8 M Q. Poisson-distributed
synaptic inputs to the dendrite were simulated using alpha
function [681 shaped current pulse injections (time constant
= 5 ms) at Poisson intervals with a mean presynaptic firing
frequency of 3 Hz.
was simulated by changing maximal synaptic conductance
At - PI) for
each presynaptic spike at time t, where P, denotes the
postsynaptic membrane potential at time t (synapses onto
inhibitory neurons were modified by an amount equal to
-AgAMPA). This simulates a temporal difference learning
rule for prediction and results in asymmetric learning
windows similar to those observed in physiological
experiments (see [29] for more details). The synaptic
conductance was adapted whenever the absolute value of
AgAMPA
exceeded 10 mV with the gain a i n the range 0.02 0.03 pS/V. The maximum value attainable by a synaptic
conductance was set equal to 0.03 p S This phenomenological model of synaptic plasticity approximates the
effects of known biophysical mechanisms such as calciumdependent and NMDA (N-methyl-D-aspartate) receptordependent induction of long-term potentiation (LTP) and
depression (LTD) (see [69] for a more detailed biophysical
implementation).
rAMpA
by an amount equal to AgAMPA
= a (Pt
+
ACKNOWLEDGMENTS
5.2. Model of Synaptic Transmission and Plasticity
Synaptic transmission at excitatory (AMPA) and
inhibitory (GABAA) synapses was simulated using first
orderkinetics of the form:
This work was supported by the Alfred P Sloan
Foundation, NIH, and Howard Hughes Medical Institute.
We are grateful to Margaret Livingstone for her
collaboration and for providing the data in Fig 76. We also
thank Dmitri Chklovskii, David Eagleman, and Christian
Wehrhahn for comments and suggestions.
/
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where r(t) denotes the fraction of postsynaptic receptors
bound to the neurotransmitter at time, t, [g is the
neurotransmitter concentration, and a and p are the
forward and backward rates for transmitter binding.
Assuming receptor binding directly gates the opening of an
associated ion channel, the resulting synaptic current can
be described as [33]:
where g,),is the maximal synaptic conductance, V,,,,(t) is
the postsynaptic potential and E,,,, is the synaptic reversal
potential. For the simulations, all synaptic parameters were
set to values that gave the best fit to whole-cell recorded
synaptic currents (see [33]). Parameters for AMPA
synapses: a = 1.1 x lo6M-Is-' ,p= 190 s-I, and EAMPA=
0
mV. Parameters for GABAAreceptors: a = 5 x lo6M-Is-',
p= 180 s-I, and EGABAA=
-80 mV. Synaptic plasticity was
simulated by adapting the maximal synaptic conductance
g,,,, for recurrent excitatory synapsesaontoboth excitatory
neurons and GABAergic interneurons according to the
learning rules described in the text. The inhibitory synapses
themselves were not adapted because evidence is currently
lacking for their plasticity. We therefore used the following
HS): 0.05 for mutual inhibition
fixed values for gGABAA(in
between the two chains and 0.016 for recurrent inhibitory
connections within a chain for the simulations in Fig 3.
Synaptic plasticity for connections onto excitatory neurons
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R A O & SEJNOWSKI : SPIKETIMING
DEPENDENT
PLASTICITY
AUTHORS
Terrence Sejnowski, PhD, is a
Howard Hughes Medical lnstitute
Investigator, Professor and Director
of the Computational Neuro biology
Laboratory at The Salk Institute. He is
also Professor of Biology and Adjunct
Professor of Physics, Neurosciences,
Psycho-logy, Cognitive Science,
Electricaland Computer Engineering,
and Computer Science and Engineering at UCSD, where
he is Director of the lnstitute for Neural Computation and
Director of training programs in Computational
Neurobiology and Cognitive Neuroscience. The goal of his
research is to build linking principles from brain to behavior
using computational models, and a combination of
theoretical and experimental approaches ranging from the
biophysical to the systems level. He is founding Editor of
"Neural Computation" and President of the Neural
Information Processing Systems (NIPS) Foundation. He is
a past recipient of the Presidential Young lnvestigator
Award, and was Wiersma Visiting Professor of
Neurobiology and a Sherman Fairchild Distinguished
Scholar at the California lnstitute of Technology where he
continues as a part-time Visiting Professor. He is a Fellow of
the IEEE and has received the Pioneer Award from the
IEEE Neural Network Society.
*
*
Rajesh P N Rao completed his high
school in Hyderabad, India in 1988
and graduated summa cum laude in
1992 with bachelor's degrees in
Compuer Science and Mathematics
from Angelo State University in
Texas. He received his M S and PhD
degrees in Computer Science from
the University of Rochester, New
York, and was an Alfred P Sloan Postdoctoral Fellow in
computational neuroscience from 1997-2000 at the Salk
lnstitute for Biological Studies.in La Jolla, California. He is
currently an assistant professor in the Computer Science
and Engineering department and in the Neurobiology and
Behaviour program at the University of Washington,
Seattle. He received a Sloan Research Fellowship for junior
faculty in 2001, an-NSF career award and a David and
Lucile Packard Fellowship in 2002, and an ONR Young
lnvestigator Award in 2003. His current research interests
span the areas of computational neuroscience, machine
learning, computer vision, robotics, and brain-computer
interfaces.